Titles and Short Summaries of the Talks

29 Geometry
Final: 2013/2/7
17 Kotaro Kawai (Tohoku Univ.) ∗ Construction of coassociative submanifolds · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: The notion of coassociative submanifolds is defined as the special class of the minimal
submanifolds in G2 manifolds. We construct coassociative submanifolds in R 7 and the anti-self-dual
bundle over the 4-sphere by using the symmetry of the Lie group action.
18 Kota Hattori (Univ. of Tokyo) ∗ Generalizations of Taub-NUT deformations · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We introduce a generalizations of Taub-NUT deformations for large families of hy-
perkähler quotients, which is already known to be defined for toric hyperkähler manifolds and ALE
spaces of type Dk.
19 Tomoyuki Hisamoto (Univ. of Tokyo) ♯ Geometry of the space of Kähler metrics, the relation between Calabitype
functionals and the Donaldson–Futaki invariant. · · · · · · · · · · · · · · · 15
Summary: Given a polarized Kähler manifold, we show that the algebraic norm of a test
configuration equals to the norm of tangent vectors of associated weak geodesic ray in the space
of Kähler metrics. Using this result, We may give a natural energy theoretic explanation for the
lower bound estimate on the Calabi functional by Donaldson and prove the analogous result for the
Kähler–Einstein metric.
20 Nobuhiko Otoba (Keio Univ.) ♯ New examples of Riemannian metrics with constant scalar curvature
· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 15
Summary: We constructed a one-parameter family of Riemannian metrics on the non-trivial
S 2 -bundle over S 2 . In a certain sense, these metrics are the counterpart of the one-parameter
family of natural product metrics on the trivial S 2 -bundle over S 2 . Every metric in the family has
the following properties: (i) its isometry group contains the special unitary group SU(2), (ii) the
projection as fiber bundle is a Riemannian submersion with totally geodesic fibers onto the round
2-sphere of some radius, and (iii) it has constant scalar curvature. We observe some of these metrics
are unique constant scalar curvature metrics in their respective conformal classes up to constant
multiplication.
21 Hajime Fujita (Japan Women’s Univ.) ♯ On an S 1 -equivariant index for symplectic manifold · · · · · · · · · · · · · · · · 15
Summary: Using a technique developed in a joint work with M. Furuta and T. Yoshida we
give a formulation of S 1 -equivariant index theory for a prequantized symplectic manifold with a
Hamiltonian S 1 -action. We explain the difference between our index and the index defined by
M. Braverman.
22 Masao Jinzenji (Hokkaido Univ.) ♯ 2 Multi-point virtual structure constants and mirror computation of CP -
Masahide Shimizu (Hokkaido Univ.) model · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · 10
Summary: In this talk, we introduce multi-point virtual structure constants for the mirror
computation of Gromov–Witten invariants of CP 2 . These constants are defined as the intersection
numbers of the compactified moduli space of quasi maps from CP 1 to CP 2 with 2 + n marked
points. Some of the generating functions of these invariants correspond to the mirror maps and the
other generating functions are translated into the generating functions of genus 0 Gromov–Witten
invariants of CP 2 . We also discuss the mirror computation of the open Gromov–Witten invariants
of CP 2 .